>> THERE YOU GO, OKAY.
SO I WAS, UH, ASKED TO TALK
ABOUT, UM, TWO DIFFERENT THINGS.
WELL, ALMOST COMPLETELY
DIFFERENT THINGS.
UM, ONE IS THE EXPERIMENTS
THAT BORIS KHUSID
AND BILL MEYER,
WHO ARE SITTING OVER THERE,
AND I DID THIS SUMMER
ON, UH, ISS.
UM, AND THE OTHER IS A-A,
UM, SYNOPSIS TO SOME EXTENT
OF A WORKSHOP THAT I RAN AT
THE AMERICAN PHYSICAL SOCIETY,
UM, FOR NASA
LOOKING AND GRAND CHALLENGES.
SO THE FIRST ONE I THOUGHT WAS
GONNA BE THE OLDEST PROBLEM
ADDRESSED AT THIS MEETING, OKAY?
WE’RE LOOKING AT A PROBLEM
PACKING OF SPHERES,
WHICH IS AT LEAST 5,000
TO 10,000 YEARS OLD.
IT STARTED WHEN PEOPLE
FIRST HAD AGRICULTURE.
AND I CAN CERTAINLY
BEAT COLD ATOMS,
WHICH ARE THE RESULT OF PHYSICS
THAT WAS DISCOVERED JUST ABOUT
100 YEARS AGO OR SO, OKAY?
BUT I CAN’T BEAT FIRE.
FIRE BEATS ME BY ABOUT
100,000 YEARS IN-IN-- WHEN-WHEN
IT BECAME AN INTERESTING PROBLEM
TO WORK ON.
SO I’M HUMBLED.
UM, OKAY, SO WHAT WE DID--
OOPS, IS THIS, UH--
DOES THAT WORK?
>> YEAH.
>> IT’S RED.
>> I THINK THAT’S--
>> DOES RED SHOW UP?
>> BUT IT’S WORKING.
>> OKAY, SO, UM, ON ISS, UH,
THIS CAST OF CHARACTERS
OVER THERE DID AN EXPERIMENT
ON THE CRYSTALLIZATION
OF HARD SPHERES.
THE CRYSTALLIZATION
OF HARD SPHERES HAS TO DO
WITH THE PACKING OF SPHERES,
AS I’LL SHOW YOU.
IT’S AN OLD PROBLEM,
AND IS THE MOST FUNDAMENTAL
FREEZING PROBLEM THAT THERE IS.
THE MOST ELEMENTARY
AND THE MOST FREEZING,
THE MOST INTUITIVE.
AND AS YOU’LL SEE,
ONE THAT HAS CREATED
A LOT OF CONFUSION
OVER MANY YEARS, PARTLY
FROM COMPUTER SIMULATIONS,
WHICH NOW ARE UNDER CONTROL.
AND BASICALLY WHAT WE DID
IS WE SHOWED THAT WE GOT A--
FOR US, I’M GONNA DO MY HANDS
LIKE THIS--
AN ENORMOUS CRYSTAL,
BUT IT’S NOT THAT BIG.
IT ACTUALLY LOOKS LIKE
A SINGLE CRYSTAL OF A--
A SINGLE FCC CRYSTAL,
FACE CENTERED CUBIC CRYSTAL,
WHICH NOBODY HAD SEEN BEFORE
ON-ON ANY SCALE TO SOME EXTENT.
THEY’VE ALWAYS SEEN CRYSTALS
THAT ARE MIXED PHASES
FOR HARD SPHERES.
AND THIS WAS ESSENTIALLY,
UH, 2.5 CENTIMETERS LONG.
AND AS FAR AS WE CAN TELL,
ALMOST PERFECT.
WE COULDN’T FIND
IMPERFECTIONS IN IT EASILY.
AND, UM, FCC, AS INDICATED HERE,
AND I’LL SHOW YOU
MORE ABOUT THIS,
SIMPLY BY CONFOCAL
AND MICROSCOPY SLICES,
WHICH SHOWED TWO FACES,
A HEXAGONAL FACE OVER HERE
AND A SQUARE FACE OVER HERE.
AND THE OTHER CONTESTANTS
FOR THE DENSEST PACKING
AND FOR THE EQUILIBRIUM
STRUCTURE OF, UH,
OF A HARD SPHERE SYSTEM, UM,
IS HEXAGONAL CLOSE PACKED,
THEN THE RANDOM HEXAGONAL
CLOSE PACKED, AND DOUBLE
HEXAGONAL CLOSE PACKED.
AND LOTS OF OTHER THINGS,
NONE OF WHICH HAD THESE
SQUARE FACES OVER HERE.
SO THAT’S ESSENTIALLY, UH,
WHAT WE LEARNED
THIS PAST SUMMER.
AND WE’RE STILL
GONNA LEARN MORE.
NOW, ACTUALLY, THIS IS BELOW--
HOW DO I GET IT SO THAT, UH,
I’M ALL ON SCREEN?
MAYBE I CAN’T.
OKAY, I’LL LIVE WITH THIS.
UM...
I-I CAN’T DO IT THIS WAY,
I DON’T THINK.
THAT DIDN’T WORK.
>> THAT’S THE PROJECTOR.
>> OH.
>> PULL THE RANGE OUT.
>> NO, YOU CAN’T, OKAY.
YOU’D HAVE TO MOVE IT CLOSER.
ANYWAY, THAT’S-THAT’S FINE.
SO, UM, WHAT WE-WHAT WE DID
IN, UH, I THINK ALMOST
TWO YEARS AGO.
IT WAS SUPPOSED TO BE
AT THE AP-- THE AMERICAN
PHYSICAL SOCIETY MARCH MEETING,
UM, IN 2020,
BUT, UM, THAT WAS POSTPONED.
THAT MEETING WAS CANCELED,
SO WE HAD IT
THE FOLLOWING SUMMER.
AND THE IDEA WAS, IT TURNS OUT,
THAT NASA WAS ONE OF THE FIRST
AGENCIES TO DISCOVER THAT
THERE WAS INTERESTING SCIENCE
TO DO IN SOFT MATTER, OKAY?
AND SO THEY WERE A MAIN FUNDING
AGENCY FOR SEVERAL DECADES,
AND THEY SPONSORED EXPERIMENTS
ON POLYMERS AND COLLOIDS,
AND EMULSIONS, AND FILMS
AND OTHER THINGS.
AND THERE WERE ALL SORTS
OF INTERESTING PHENOMENA
THAT WERE STUDIED.
UM, CONTINUE TO BE STUDIED.
UH, THEY WANTED TO KNOW.
THE IDEA OF THIS
WAS TO FIND OUT,
WELL, WHAT’S NEXT?
WHAT ARE WE GONNA DO--
THAT WAS LAST CENTURY.
WHAT ARE WE GONNA DO
IN THE 21ST CENTURY
THAT’S REALLY NEW, RIGHT?
AND, UM, THE BASIC IDEA WAS
NON-EQUILIBRIUM PHENOMENA.
EQUILIBRIUM PHENOMENA
ARE 19TH/20TH CENTURY.
IT’S A SOLVED PROBLEM, OKAY?
NON-EQUILIBRIUM PHENOMENA,
THERE ARE NO RULES, RIGHT?
ALL WE KNOW IS
SOMETIMES NEWTON’S LAWS WORK.
SOMETIMES THEY DON’T, OKAY?
IN PARTICULAR, FOR EXAMPLE,
ONE OF THE NEW THINGS
THAT PEOPLE ARE STUDYING
IN SOFT MATTER PHYSICS ARE
WHAT ARE CALLED NON-RECIPROCAL
INTERACTIONS, OKAY?
SO RECIPROCAL INTERACTIONS
ARE NEWTON’S SECOND LAW.
IF I HAVE A FORCE
FROM THIS ON THIS,
I HAVE THE OPPOSTIE FORCE
ON THIS FROM THAT, RIGHT?
OKAY, BUT THAT’S
NOT ALWAYS THE CASE WHEN
YOU DEAL WITH ACTIVE SYSTEMS,
WITH NON, UM, UH,
NON-EQUILIBRIUM SYSTEMS.
FOR INSTANCE,
IF SOMEBODY’S CHASING YOU,
YOU’RE REPELLING THEM,
THAT IS YOU’RE TRYING
TO GET AWAY FROM THEM.
YOU’RE MOVING IN ONE DIRECTION,
AND THEY’RE CHASING AFTER YOU,
AND YOU’RE BOTH GOING
IN THE SAME DIRECTION
RATHER THAN GOING
IN OPPOSITE DIRECTIONS,
WHICH IS WHAT
NEWTON WOULD SAY.
AND THAT’S BECAUSE THERE ARE
OTHER FORCES WHEN YOU HAVE
NON-EQUILIBRIUM PHENOMENA
GOING ON.
OKAY, SO THERE ARE
ALL SORTS OF, UM,
NEW WAYS OF MAKING MATERIALS.
UM, WHAT-WHAT WE’VE FOUND IS
THAT ASIDE FROM A THEME BEING,
UM, NON-EQUILIBRIUM PHENOMENA,
ANOTHER THEME THAT CAME UP,
WHICH WE’LL PROBABLY--
I’LL GO FURTHER INTO LATER
IS ARTIFICIAL LIFE,
BECAUSE IT TURNS OUT
SOFT MATTER PHYSICS
IS ESSENTIALLY STUDYING
HOW THE MATERIALS
THAT MAKE UP LIFE WORK, RIGHT?
AND HOW, WITH
NON-EQUILIBRIUM PHENOMENA,
YOU MAY BE ABLE TO GET
SOMETHING LIKE LIFE,
RATHER THAN BIOPHYSICS,
WHICH IS SOMETHING WHICH TRIES
TO DISSECT LIFE AND FIND OUT
MECHANICALLY HOW IT WORKS.
OKAY, SO SOME OF THE THINGS
WE’VE FOUND ARE YOU CAN MAKE
DIFFERENT KINDS OF MATERIALS.
DNA IS A GREAT TOOL.
DNA NOW IS A GLUE.
PEOPLE, YOU CAN BUY DNA FROM
LOTS OF DIFFERENT COMPANIES.
YOU CAN PUT IT ON PLASTICS.
YOU CAN PUT IT ON EMULSIONS.
YOU CAN PUT IT ON COLLOIDS.
YOU CAN PUT IT IN GELS, OKAY?
AND THE BIG ADVANTAGE OF DNA
AS YOU KNOW,
IT ONLY BINDS SPECIFICALLY
WITH ITS COMPLEMENT.
AND SO YOU DON’T HAVE TO
D-DESIGN NEW CHEMISTRIES
TO GET THINGS TO STICK TOGETHER
IN DIFFERENT WAYS.
YOU CAN JUST BUY DNA,
ATTACH IT AS, YOU KNOW,
ATTACHING SPECIFICALLY
TO YOUR MATERIALS,
AND ASSEMBLE THE MATERIALS
THAT WAY.
SO FOR INSTANCE, YOU CAN MAKE,
UM-- LET’S SEE, DOES THIS--
DOES THIS RUN-- OOPS!
THIS DOESN’T CONTROL IT.
THIS CONTROLS IT.
NO, THAT’S NOT WHAT I WANTED.
OKAY, LET ME GO BACK.
I DON’T HAVE CONTROL FROM THIS.
ANYWAY, YOU CAN STRING
EMULSIONS TOGETHER.
I’M GONNA SHOW YOU SOME
STUFF WITH THAT.
YOU CAN STUDY, UM,
FOLDING PROBLEMS.
YOU CAN CREATE THINGS
WITH NEW MATERIALS
BY FOLDING LINEAR CHAINS.
YOU CAN ALSO FOLD SHEETS.
YOU CAN ALSO LEARN FROM THAT
ABOUT HOW PROTEINS FOLD.
UM, THIS IS SOMETHING
THAT’S REALLY RECENT.
THIS IS, UH, THE WORK OF ONE
OF MY COLLEAGUES, DAVE KLEIN,
WHO IT TURNS OUT,
THE BEST MATERIALS
FOR MAKING PHOTONIC BAND GAPS
ARE DIAMOND LATTICE.
BUT YOU HAVE TO MAKE
A DIAMOND LATTICE
ON THE SCALE OF MICRONS.
AND THE STANDARD THING TO DO
TO MAKE THINGS
ON A MICRON SCALE,
AS IN THE EXPERIMENTS
THAT WE DID THIS SUMMER,
USED COLLOIDS.
BUT HARD SPHERES WILL DO IT.
THEY’LL MAKE YOU AN FCC LATTICE,
WHICH IS NOT A DIAMOND LATTICE.
AND A DIAMOND LATTICE IS REALLY
A-A-A VERY SPARSE LATTICE.
RIGHT? BECAUSE EACH PARTICLE
HAS FOUR NEIGHBORS, WHICH
IS A VERY, VERY LOW NUMBER
OF-OF NEIGHBORS, OKAY?
BUT USING DNA, UM,
THEY MADE THIS CRYSTAL,
AND IT’S NOT GREAT, RIGHT?
THESE-- THIS IS MAYBE, UH,
LET’S SAY 40 MICRONS ACROSS
BY 40 MICRONS.
WHAT WE’VE FOUND IN MICROGRAVITY
THIS SUMMER IS YOU CAN MAKE
COLLOIDAL CRYSTALS THAT ARE
MUCH, MUCH BIGGER THAN THAT
WHEN YOU GET RID OF GRAVITY.
GRAVITY IS-IS ANATHEMA TO MAKING
BIG COLLOIDAL CRYSTALS.
OKAY, ANOTHER THEME
THAT CAME OUT WAS, UH,
ASIDE FROM NEW MATERIALS
AND NON-EQUILIBRIUM IS
MACHINES MADE OUT OF MACHINES.
THAT SOUNDS KINDA FUNNY, RIGHT?
BUT OF COURSE, YOU ARE A MACHINE
MADE OUT OF MACHINES, RIGHT?
EVERY ONE OF YOUR CELLS, OKAY,
IS EFFECTIVELY A MACHINE.
IT HAS A METABOLISM.
IT’S TRANSDUCING WORK, ENERGY,
CHEMICAL ENERGY,
DIFFERENT KINDS, RIGHT?
AND THEN YOU’RE BUILT
UPON THE COLLECTION.
ON AN ELEMENTARY LEVEL,
THERE ARE SEVERAL EXAMPLES
OF THIS WHICH ARE
COMING UP AGAIN.
I CAN’T DO IT WITH THIS.
SO THIS LAST ONE HERE,
I’LL SHOW YOU MORE ABOUT LATER.
BUT THESE ARE-- OOPS!
ACTUALLY I CAN DO IT LIKE THAT.
ARE PARTICLES WHICH SPIN, OKAY?
THEY'RE LITTLE MAGNETIC
PARTICLES WHICH SPIN.
IT TURNS OUT IF YOU HAVE AN
INDUCED DIPOLE,
AND YOU ROTATE IT
IN PLANE, YOU GET
AN ATTRACTIVE INTERACTION.
IF YOU ROTATE
IN THREE DIMENSIONS,
YOU GET NOTHING, OKAY?
BUT IN TWO DIMENSIONS,
YOU GET IT.
YOU SEE THESE GUYS
FORM A LIQUID.
IT’S WHAT’S CALLED
AN ODD LIQUID, AND WE’LL SEE
MORE OF THIS LATER,
IN THE SENSE THAT
WHEN YOU PUSH IT IN, IT SHEERS.
IT MOVES IN A SHEER DIRECTION.
IT’S ODD IN THE SAME SENSE
THAT A HALL RESISTANCE
IS-IS ODD COMPARED TO A--
IT’S AN OFF-DIAGONAL RESISTANCE.
IN THE SAME WAY, THIS IS
AN OFF-DIAGONAL ELASTICITY
AND VISCOSITY, AND WE’LL SEE
MORE OF THAT LATER.
OKAY, SO LET ME GET STARTED,
INSTEAD OF SPENDING
ALL MY TIME ON THE FIRST SLIDE.
OKAY, HERE’S THE OLD PROBLEM,
OKAY? SO THIS IS
A SPHERE PACKING PROBLEM.
MONODISPERSED UNIFORM
HARD SPHERES.
NO INTERACTION BETWEEN THEM
EXCEPT THEY DON’T OVERLAP, OKAY?
THEY HAVE EXCLUDED
VOLUME EFFECTS.
UM, LET’S SEE HOW I CAN DO THIS.
SO, UM, THIS--
OH, WE’RE MISSING--
YEAH, NOW-NOW WE’RE MISSING
THE TOP.
ANYWAY, THE IMPORTANT THING
IS HALES.
UM, SO, UH, THE PROBLEM,
AS-AS YOU GUYS PROBABLY KNOW IT,
FOR THE DENSEST PACKING
OF SPHERES IS-IS CALLED
A KEPLER CONJECTURE,
‘CAUSE HE WAS PAID
BY THE BRITISH GOVERNMENT
TO SEE HOW MANY CANNONBALLS
HE COULD GET ON
NAVAL SHIPS, RIGHT?
UM, THE SOLUTION TO THE PROBLEM,
UM, WAS FIRST SORT OF DONE
BY GAUSS, WHO SHOWED
THAT AMONG THE LATTICES,
THE FCC LATTICE WAS
THE DENSEST LATTICE.
AND THE PROOF THAT YOU DIDN’T
HAVE NON-LATTICE STRUCTURES
THAT COULD BEAT FCC
WAS DONE BY THOMAS HALES,
UM, IN 1994.
THE PROOF TOOK 10 YEARS
TO PASS THE REFEREES,
‘CAUSE IT’S PARTIALLY
A COMPUTER PROOF.
OKAY, UH, IN ONE DIMENSION,
YOU JUST TOUCH YOUR PARTICLES
TOGETHER IN A LINE OVER HERE.
IF YOU NOW WANNA GO
TO TWO DIMENSIONS,
WHAT YOU DO IS YOU STACK
THE LINES ON TOP OF ONE ANOTHER,
BUT YOU DON’T STACK THEM
ONE CENTER ABOVE THE OTHER.
YOU SLIDE IT OVER
SO YOU FIT IN THE SPACES
HERE BELOW THE FIRST ONE.
AND THAT GIVES YOU
HEXAGONAL LATTICE,
AND THAT'S THE DENSEST PACKING
IN TWO DIMENSIONS.
IF YOU WANNA GO
TO THREE DIMENSIONS,
YOU DO THE NEXT THING
WHICH IS YOU TAKE THIS LAYER
AND YOU STACK IT ON TOP.
BUT AGAIN, YOU PLAY THE TRICK,
OKAY, THAT YOU DON’T PLACE IT
DIRECTLY ON TOP.
YOU SLIDE IT OVER
INTO THE INTERSTICES UNDERNEATH,
WHICH MEANS YOU PUT THAT SPHERE,
LET’S SAY, OVER THERE,
OVER THERE,
AND THAT SPHERE OVER THERE,
AND THAT SPHERE OVER THERE.
BUT YOU HAVE A CHOICE,
BECAUSE YOU COULD’VE
PUT THIS GUY INSTEAD OF--
LEMME SEE WHERE I AM--
INSTEAD OF PUTTING IT
FROM THERE TO THERE, OKAY?
FROM ON TOP TO THERE,
YOU COULD’VE GONE THAT WAY.
SO THERE ARE TWO WAYS
OF DOING IT.
SO THERE ARE THREE
SEPARATE PLANES AND STACKING.
AND IF YOU MAKE THE STACKING,
UM, A-B-C, A-B-C, A-B-C,
AS WE’LL SEE LATER,
THAT GIVES YOU
THE FACE-CENTERED
CUBIC STRUCTURE,
WHICH IS THE MOST COMMON
STRUCTURE OF THE ELEMENTS, OKAY?
BUT IF YOU GO A-B, A-B, A-B,
YOU GET HEXAGONAL CLOSE PACKED,
WHICH HAS EXACTLY
THE SAME DENSITY, OKAY?
BUT IS, UM-- THIS ACTUALLY
IS MAYBE THE THIRD DENS--
UM, MOST COMMON OF THE ELEMENTS.
BUT IF ANYTHING,
YOU HAVE THAT CHOICE,
AND IN FACT, YOU GET
THE SAME DENSITY INDEPENDENT
OF HOW YOU STACKED THEM.
YOU CAN STACK IT A-B-A-B.
THAT'S HEXAGONAL.
YOU CAN STACK IT A-B-A-C.
THAT'S DOUBLE HEXAGONAL.
CLOSE PACKED,
WHICH IS LANTHANUM STRUCTURE.
YOU CAN ALSO DO A-B, A-C-B--
AS LONG AS YOU ALTERNATE LAYERS.
DON'T HAVE THE SAME THING.
OKAY, SO THAT PROBLEM
IS KNOWN.
UM, IT WAS KNOWN
FOR THOUSANDS OF YEARS,
AS SOON AS PEOPLE HAD FRUIT.
GROCERS KNEW IMMEDIATELY
THAT THE WEIGHT TO STACK
THE FRUIT BEST, OKAY?
IS THE FCC STRUCTURE.
AND IT'S STILL USED,
OBVIOUSLY, BY GROCERS.
SO THAT PROBLEM,
EVEN THOUGH IT WASN'T PROVED,
PROVEN, WAS KNOWN.
THE ANSWER WAS KNOWN FOR
LITERALLY THOUSANDS OF YEARS.
NOW, IF YOU LOOK AT THE SIDE
OVER HERE-- LET ME SEE.
DO I HAVE THIS RIGHT?
NO, I DON'T.
ANYWAY, IF YOU LOOK AT THE, UM--
YEAH, I DO.
YOU CAN'T SEE THIS.
UH, SHOW ME BELOW.
UM, IF YOU LOOK
OVER HERE,
YOU GET WHAT HAPPENS
IF YOU TAKE YOUR PARTICLES
OR YOUR FRUIT
AND YOU JUST POUR IT INTO A BOX
AND YOU DON'T ORDER IT,
EITHER BY A SPECIAL PROTOCOL
OF SHAPING, OR BY PLACING THEM
DOWN ONE BY ONE. OKAY?
AND THIS GUY OVER HERE, UM,
IT WAS STUDIED
IN THE LAST CENTURY BY BERNAL
WHO THOUGHT THAT IT WAS
THE STRUCTURE OF LIQUIDS,
WHICH IT ISN'T, OKAY?
BUT IT WAS CALLED
RANDOM CLOSE PACKING, RCP.
ITS DENSITY IS LOWER.
FCC PACKS THE 74%.
THIS PACKS THE 64%.
AND THIS IS AN EQUALLY OLD
AND IMPORTANT PROBLEM,
ESPECIALLY IN MESOPOTAMIA
WHEN AGRICULTURE CAME AROUND,
BECAUSE BEFORE THEY HAD SCALES,
THEY SOLD FRUIT OR SEEDS
OR WHATEVER BY VOLUME.
AND IF YOU COULD FIND A WAY
TO PACK LESS DENSE
THAN THIS, RIGHT?
THEN YOU'LL SELL MORE STUFF.
YOU'LL GET RICH.
YOU CAN BUY
YOUR NEIGHBOR'S FARM.
IT WAS IMPORTANT.
AND IT'S EVEN MENTIONED
IN THE BIBLE.
IT'S EVEN MENTIONED IN THE BIBLE
THAT IT IS WRONG,
UNLESS YOU PRESS DOWN
AND SHAKE TOGETHER YOUR STUFF
TO GET THE DENSEST PACKING.
SO THIS IS-IS AN EQUALLY
OLD PROBLEM.
THIS ONE IS NOT UNDERSTOOD
THE WAY THAT THAT ONE IS.
THE DENSEST PACKING
IS WELL UNDERSTOOD.
THIS ONE ISN'T.
UM, JUST TO GIVE YOU AN EXAMPLE,
THERE ARE TWO PAPERS HERE,
ONE OF WHICH YOU CAN'T SEE,
WHICH IS FROM OUR GROUP,
WHICH WAS A PHYS REV LETTER
IN 2021, WHICH HAD--
WHICH WAS RIGHT UNDER THIS ONE.
IT'S 38002.
THAT'S OUR--
THERE YOU GO. OKAY.
I CAN'T STRETCH IT DOWN.
ANYWAY, BUT YOU SHOULD NOTE
THAT THIS IS--
YOU CAN TELL THAT THIS IS
AN INTERESTING PROBLEM,
BECAUSE THIS PAPER THAT WAS
JUST BEFORE OURS
HAS AS ITS SENIOR AUTHOR
GIORGIO PARISI,
WHO IS ONE OF THE GUYS WHO WON
A NOBEL PRIZE THIS YEAR
IN PHYSICS, OKAY?
UM, SO THESE ANCIENT PROBLEMS,
YOU KNOW, ARE STILL OF INTEREST
TO FAIRLY GOOD PEOPLE.
ANYWAY, I DON'T COUNT MYSELF
AMONG THEM, BUT PARISI IS.
UM, OKAY, NOW WHY
IS THIS INTERESTING?
WHY IT IS INTERESTING
THAT DISORDER IS LESS DENSE
THAN THE ORDER?
AND BY THE WAY, IT IS
AN INTERESTING PROBLEM
AS FUNDAMENTAL AS ASKING
WHETHER THE GROUND STATE
OF PHYSICAL SYSTEMS IS
INTRINSICALLY ORDERED OR NOT.
THE QUESTION YOU COULD ASK
IS FOR MINOR DISPERSED PARTICLES
OF ANY SHAPE WHATSOEVER.
DO YOU EVER GET
A DISORDERED PHASE,
WHICH IS HIGHER DENSITY
THAN THE ORDERED PHASE?
AND NOBODY'S FOUND
SOMETHING LIKE THAT YET,
BUT NOBODY'S PROVEN
THAT YOU CAN'T HAVE IT.
HERE'S WHY IT'S
AN INTERESTING PROBLEM.
AND AGAIN, THE TOP IS
CUT OFF HERE.
WHAT'S SUPPOSED TO BE UP ON TOP
IS SOMETHING THAT YOU ALL
LEARNED IN PUBLIC SCHOOL,
WHICH IS THE IDEAL GAS LAW,
WHICH IS PV = nRT. RIGHT?
AND EVERYBODY KNOWS THAT.
AND THAT'S FOR AN IDEAL GAS,
AND IDEAL GAS IS POINT PARTICLES
THAT PASS THROUGH ONE ANOTHER.
WHEN VAN DER WAALS,
AND IT SHOULD SAY VAN DER WAALS
UP THERE, UM...
WHEN VAN DER WAALS
FIRST STARTED LOOKING
AT INTERACTING GASSES, HE SAID,
WELL, YOU CAN INCLUDE
ATTRACTIVE INTERACTIONS,
BUT THE THING
YOU OUGHT TO DO FIRST,
THE FIRST THING TO CONSIDER IS
THAT PARTICLES TAKE UP VOLUME.
EVEN CLASSICAL PARTICLES, OKAY?
IT'S NOT FRUIT.
IT'S ALL-- IT'S ALL RELATED,
OF COURSE, TO QUANTUM MECHANICS,
BUT AT ANY EVENT,
CLASSICAL PARTICLES
TAKE UP VOLUME.
THERE'S EXCLUDED VOLUME,
AND THEREFORE,
WHAT VAN DER WAAL SAID IS,
WELL, THE FIRST THING
YOU SHOULD DO IS YOU SAY
THE VOLUME THAT YOU HAVE
TO MOVE AROUND IN
ISN'T THE VOLUME
OF YOUR CONTAINERS.
THE VOLUME OF YOUR CONTAINER
MINUS THE NUMBER OF PARTICLES
TIMES THEIR VOLUME.
AND IF I FACTOR OUT
THE V FROM THIS,
THIS BECOMES 1 - 5/5C,
WHERE 5C IS THE DENSEST PACKING,
RIGHT?
SO WHAT THAT TELLS YOU,
ACCORDING TO THIS,
WHEN I JUST DIVIDE THROUGH
IS THAT...
CLOSER.
IS IT CLOSE ENOUGH?
LET ME JUST SEE.
YES, ALMOST CLOSE ENOUGH.
YOU CAN ALSO RAISE
THE FRONT, RIGHT?
WITH THAT-- WITH THAT.
THANKS.
SORRY.
ANYWAY, UM...
[ CHUCKLES ]
TOO MUCH OF A PROBLEM.
ACTUALLY, CAN'T YOU--
CAN'T YOU CHANGE THE--
DOESN'T THE LENS CHANGE
IN FRONT?
>> PAUL, I THINK THIS IS
ANOTHER ANCIENT PROBLEM.
[ LAUGHTER ]
>> ABSOLUTELY.
I DON'T THINK IT'S BAD
AS FAR AS FIRE, THOUGH, GOES.
THAT'S HARD TO BEAT.
THAT EVEN BEATS
THE BOW AND ARROW, I THINK.
FIRE.
ANYWAY, UM, OKAY.
I THINK THAT-- I THINK THAT'S
GOOD ENOUGH FOR NOW.
THANKS. OKAY.
SO HERE'S WHAT HAPPENS.
WHAT THIS THING TELLS YOU IS
IF THE VOLUME-- THIS DIVERGES,
THE PRESSURE DIVERGES AT THE--
JUST AS YOU APPROACH
THE CRITICAL PACKING DENSITY.
OKAY?
SO IF I HAVE
A DISORDERED SYSTEM,
LIKE THE SPHERES,
I DIDN'T PUT DOWN
AN ORDER FOR THEM.
THE PRESSURE DIVERGES AT 64%,
WHEREAS THE ORDERED STATE
DIVERGES AT 74%.
SO SOMEWHERE, THESE GUYS CROSS,
AND FOR SURE,
AS YOU APPROACH 64%,
YOUR PRESSURE IS HIGHER
IN THE DISORDERED PHASE
THAN IT IS IN THE ORDERED PHASE,
THE CRYSTALLINE PHASE,
SO THE PARTICLES ACTUALLY
GET PUSHED BY PRESSURE, OKAY?
FROM THE DISORDERED PHASE
TO THE ORDERED PHASE
WHERE THEY HAVE MORE ROOM TO--
MORE ROOM TO MOVE AROUND, OKAY?
AND THAT ESSENTIALLY--
YOU COULD DO THIS--
THE SAME ARGUMENT
IN TERMS OF ENTROPY.
YOU CAN SAY, WELL,
THE HIGHER DENSITY PHASE
AND THE PARTICLES HAVE MORE ROOM
IF THEY ORGANIZE IN THAT WAY,
HAVE MORE ROOM TO MOVE AROUND
THAN THEY DO WHEN
THEY'RE JAMMED, IF YOU LIKE,
IN THE DISORDERED PHASE
BECAUSE THEY'RE ESSENTIALLY
GETTING CLOSE TO 64.
SO THE ENTROPY IS HIGHER
IN THE ORDERED PHASE
THAN THE DISORDERED PHASE
BECAUSE OF THE FREE VOLUME.
ANYWAY, THE PRESSURE DRIVES
THE LIQUID TO THE CRYSTAL.
THAT SAYS THAT SOMEWHERE
BEFORE YOU REACH .64,
YOU HAVE TO FORM
A CRYSTAL, OKAY?
AND THAT'S THE EASIEST,
MOST FUNDAMENTAL FREEZING
TRANSITION THERE IS.
IT JUST INVOLVES ENTROPY.
SO PEOPLE LOOKED AT THIS
AND THEY MADE A PHASE DIAGRAM
FROM SIMULATIONS, OKAY?
AND UP TO ABOUT 1995,
THE PHASE DIAGRAM
LOOKED LIKE THIS.
HERE IS RANDOM CLOSE PACKING.
OKAY? THAT'S 63-64.
HERE'S CRYSTAL CLOSE
PACKING-- 74.
SOMEWHERE BEFORE
YOU GET TO THE 64,
YOU'RE SUPPOSED TO GO
TO A CRYSTAL, OKAY?
AND YOU HAVE A LIQUID
UP TO ABOUT 50% OF CRYSTAL
ABOVE COEXISTENCE
IN THIS REGION,
AND THEY ALSO HAD
IN THE PHASE DIAGRAM
FROM THE SIMULATIONS,
A GLASS PHASE THAT WAS IN THERE.
SOMEHOW THINGS GOT STUCK
AND BECAME GLASSY.
UM, OKAY.
SO THAT'S WHAT THE SIMULATION
PHASE DIAGRAM LOOKED LIKE, OKAY?
SO THERE WERE EXPERIMENTS.
THE EXPERIMENTS IN THE MID-80S.
THIS CLASSIC EXPERIMENT
BY PETER PUSEY AND VAN MEGEN,
UM, LOOKED AT COLLOIDS.
OKAY, THIS IS BACKWARDS.
THE LOW DENSITY IS HERE,
AND THE HIGH DENSITY
IS OVER HERE.
THERE'S A LIQUID OVER HERE.
THIS IS COEXISTENCE OVER HERE,
AND OVER HERE, AND OVER HERE.
HERE IT'S ALL CRYSTALLINE.
YOU CAN TELL
THAT IT'S CRYSTALLINE
BECAUSE WHEN IT'S CRYSTALLINE,
YOU BRAGG SCATTER
VISIBLE LIGHT BECAUSE THIS--
THE UNIT CELL IS LIKE
THE WAVELENGTH OF LIGHT.
OKAY, SO THE COLORS HERE
ARE BRAGG SCATTERING.
HERE YOU SEE THE LESS--
A PHASE FLOATING ABOVE A PHASE.
THIS IS CRYSTAL.
THIS IS A HIGHER DENSITY,
SO I CALLED IT A GLASS
BECAUSE SUPPOSEDLY IT WAS RIGID.
UM, AND THAT'S WHAT
THE PHASE DIAGRAM LOOKED LIKE.
OKAY, WE DECIDED TO TRY IT,
TO GET RID OF THIS
GRAVITATIONAL SEDIMENTATION
AND DO IT IN MICROGRAVITY.
SO THERE ARE A BUNCH
OF EXPERIMENTS THAT WERE DONE
IN, UH, THE EARLY 90S,
I GUESS, TO MID 90S,
UM, ON THE SHUTTLE.
THIS WAS PHASE.
THIS WAS ONE OF THEM.
COLLOIDAL DISORDER,
ORDER TRANSITION, GELATION.
THERE'S ANOTHER ONE HERE,
IS WHAT OUR PHASE DIAGRAM
LOOKED LIKE, SO AGAIN,
IT WAS LIQUID DOWN HERE.
YOU CAN SEE CRYSTALLIZED
GROWING DOWN HERE.
ACTUALLY, THE CRYSTALLIZED
IN MICROGRAVITY GREW DIFFERENTLY
THAN THEY DO IN GRAVITY.
IN GRAVITY, YOU HAVE
NUCLEATION AND GROWTH
FROM SORT OF SPHERICAL CENTERS.
THAT'S THE CLASSICAL
NUCLEATION GROWTH.
HERE, THERE'S INSTABILITY
AND YOU GET DENDRITES
GROWING FIRST.
THAT WASN'T SO INTERESTING.
IT WAS STARTLING,
BUT IT WASN'T AS INTERESTING
AS THE FOLLOWING.
AS WE WENT UP HERE,
EVERYTHING CRYSTALLIZED.
THERE WAS NO GLASS PHASE
THAT WAS OBSERVED,
AND IN MICROGRAVITY,
NO GLASS PHASE IS SEEN
SINCE THESE EXPERIMENTS AS WELL.
OKAY, UM, THIS IS
THE DENDRITIC GROWTH.
I WON'T SPEND TIME ON THAT.
THIS IS A SAMPLE,
IT TURNS OUT,
WHEN WE'VE GOT THESE
SAMPLES BACK NOW.
AND THAT EXPERIMENT
ONLY DID THE FOLLOWING.
IT ONLY TOOK DIFFERENT
CONCENTRATIONS IN THESE TUBES
AND TOOK PICTURES OF THEM
IN MICROGRAVITY
AS THEY CRYSTALLIZED,
OR DID WHAT THEY WERE GONNA DO.
OKAY, THE ONLY ONE THAT SURVIVED
WAS ONE OF THE REALLY
HIGH DENSITY SAMPLES.
WELL, 60%, OKAY?
THAT SURVIVED LANDING,
AND WITHOUT MELTING.
WITHOUT BEING SHAKEN UP
AND MELTING, 'CAUSE, YOU KNOW,
ON REENTRY, THERE'S LOTS OF--
IT'S NOT MICRO-G ANYMORE.
SO IT TURNS OUT THE WHOLE
THING WAS CRYSTALLINE,
AND WE THOUGHT, WELL,
WE BETTER CHECK THIS GUY OUT
BECAUSE MAYBE WE GOT
THE CONCENTRATION WRONG
AND STUFF LIKE THAT,
AND MAYBE THERE REALLY IS
A GLASS AT THIS HIGH DENSITY,
SO ONCE WE HAD THE SAMPLE
BACK ON EARTH,
WE DIDN'T WANT TO REMIX IT,
BECAUSE IF IT ONLY
CRYSTALLIZES IN SPACE,
WE WON'T GET IT BACK, RIGHT?
FOR ANOTHER TEN YEARS
OR SOMETHING LIKE THAT.
NEXT MISSION WE HAVE,
SO WHAT WE DID
IS WE MIXED HALF OF IT.
THE BOTTOM HALF.
AND THE BOTTOM HALF,
YOU CAN SEE, IS CLEAR--
IS CLEARLY A SOLID, OKAY?
HOW DO I KNOW IT'S A SOLID?
THIS IS THE STIR BAR,
AND THE BOTTOM OF THE CONTAINER
IS DOWN HERE.
AND THIS HAS BEEN
SITTING OVER HERE
FOR ABOUT A YEAR,
AT LEAST WHEN THE PICTURE
WAS TAKEN.
SO THIS IS SOLID, OKAY?
WE SEE THE CRYSTAL
GROW INTO THE GLASS,
SO THE CRYSTAL'S MORE STABLE.
SO EVER SINCE
THOSE EXPERIMENTS,
THIS IS NOT IN ANYBODY'S
PHASE DIAGRAM,
EVEN IN THE SIMULATIONS.
NOW, I DON'T WANT TO SAY
THAT WE DID IT--
WE GOT TO THE SIMULATORS
TO DECIDE THIS WAY,
OR CHANGE THE SIMULATIONS.
IT'S SIMPLY THE FACT
THAT BY THEN,
THE COMPUTERS WERE MUCH FASTER
AND MUCH HIGHER MEMORY
SO THEY COULD DO
BIGGER SYSTEMS, OKAY?
AND SO THEY FOUND, IN FACT,
THAT THEY WERE WRONG
IN EVEN THE SIMULATIONS.
YOU DON'T SEE A GLASS ANYMORE,
UM, [ INDISTINCT ].
SO HERE'S WHAT
I WAS TELLING YOU BEFORE.
IF I LOOK AT THIS STACKING
OF THIS-- DENSE STACKING,
I CAN DO IT TWO WAYS.
SO HERE'S A LAYER,
A HEXAGONAL LAYER OVER HERE.
I'VE GOT ANOTHER LAYER
ON TOP OF IT, WHICH SITS,
LET'S SAY, COVERING THESE HOLES.
THAT'S, UH, A WITH B ON TOP
OF IT COVERS THOSE--
THE HOLES THAT ARE COVERED HERE.
IF I SLID DOWN THE OTHER WAY
WITH THE NEXT LAYER,
I COVER UP THOSE HOLES,
AND THESE GUYS
WOULD BE OPENED UP
SO I COULD SEE STRAIGHT THROUGH,
AND SO IF I DO A-B-C,
I BLOCK EVERYTHING,
AND THIS A-B-C, A-B-C.
A-B-C IS THE FACE CENTERED
CUBIC STRUCTURE,
AND IF I JUST DO A-B-A-B,
I'LL GET A STRUCTURE THAT
LOOKS LIKE THIS,
WHICH HAS HOLES THROUGH IT,
AND HAS NOTHING
THAT LOOKS LIKE A CUBE IN IT.
OVER HERE, YOU CAN SEE
THIS CUBE, OKAY?
WITH A SQUARE FACE
WITH A PARTICLE
IN THE MIDDLE OF IT, RIGHT?
AND THAT’S INDICATIVE
OF AN FCC LATTICE,
AND ALL THE EXPERIMENTS
THAT WERE DONE BEFORE,
INCLUDING PUSEY’S EXPERIMENT--
OKAY, THE CLASSIC ONE
THAT STARTED A LOT OF THIS--
WAS RANDOM HEXAGONAL
CLOSE-PACKED.
THAT IS THE LAYERS
WERE RANDOMLY STACKED.
OKAY, SO HERE’S OUR EXPERIMENT
IN SPACE. THE OBJECTIVE--
A FEW OF THE PEOPLE.
THERE’S BORIS OVER THERE.
THERE IS BILL OVER THERE.
UM, I’M OVER HERE.
THE EXPERIMENT WAS DONE, UM,
WITH A CONFOCAL MICROSCOPE.
A CONFOCAL MICROSCOPE
IS A SCANNING
FLUORESCENT MICROSCOPE,
SO IT HAS, UM-- IT-IT SCANS
USUALLY IN THE PLANE,
AND THEN YOU CAN LOWER IT
AND FOCUS ON THE NEXT LAYER
AND SCAN.
SO YOU CAN GET 3-D IMAGES.
YOU CAN GET STACKS.
THE SAMPLE CELL HELD
THREE SAMPLES LIKE THIS.
THE SAMPLES WERE CAPILLARY TUBES
THAT WERE MAYBE 5 CENTIMETERS
LONG ALL TOGETHER,
2 MILLIMETERS WIDE,
AND .2 MILLIMETERS THICK.
UM, THE CONFOCAL IS MOUNTED
INTO THE LOOSE INTEGRATED RACK,
UM, AND-- LEMME SEE, UH,
WHEN I CAN DO THIS.
THIS IS-THIS IS
WHAT WAS REALLY COOL,
BUT I GET A LITTLE BIT DIZZY
IN THIS ONE WHEN I--
WHEN I LET THE MOVIE RUN.
SO HERE IS WHAT I’M SHOWING YOU.
THIS IS ONE END OF THE SAMPLE.
THIS IS THE OTHER END
OF THE SAMPLE
IN THE CAPILLARY FROM SCANS.
WHAT WE DID IS
WE DID OVERLAPPING SCANS,
INTERPRETED, THANKFULLY,
AND PIECED TOGETHER BY BORIS,
A STUDENT.
SO HERE YOU SEE
THE OVERLAPPING REGION
FROM ONE TO THE NEXT,
AND THE AMAZING THING HERE
IS, WELL, LOOK.
UM, FIRST OF ALL, YOU CAN SEE
THE HEXAGONAL PATTERNS.
IT’S CLEARLY GOT
A HEXAGONAL PATTERN
IN THESE PLANES.
NEXT, WHAT YOU CAN SEE
IS THE ORIENTATION
IS APPROXIMATELY, UM,
ALIGNED WITH ONE EDGE
OF THE CAPILLARY.
NOW, AS YOU GO DOWN, OKAY?
HERE WHAT YOU SEE
IS STILL OVERLAPPING,
STILL HEXAGONAL,
AND ESSENTIALLY ALIGNED
WITH THE BAT-- WITH THE BOTTOM
OF THE CAPILLARY.
HERE, AGAIN,
THAT’S WHAT WE’RE SEEING.
ALL THE WAY,
OVERLAPPING, ONE TO ONE.
ALL THE WAY TO THE OTHER END
OF THE CAPILLARY.
OOPS, NOTHING THERE.
OKAY, THERE’S A LITTLE BIT
OF TILT.
IF YOU LIKE, THAT’S JUST
A LONG RANGE DISTORTION
OF THE CRYSTAL.
IT’S LIKE A SYSTEM,
IF YOU DO MAGNETISM,
WHICH HAS SPIN WAVES IN IT.
RIGHT?
THERE’S SOME RIGIDITY
THAT YOU CAN, UH--
SOME ELASTICITY
THAT YOU CAN TAKE TO CHANGE
THE ORIENTATION SLIGHTLY
AS YOU MOVE DOWN.
SO IT’S HEXAGONAL.
IT LOOKS ESSENTIALLY
LIKE A SINGLE CRYSTAL.
THERE ARE PROBABLY
DEFECTS IN THERE,
LIKE THIS LOCATION.
THERE ARE DISCLINATIONS IN IT,
UM, BUT THEY’RE REALLY
HARD TO FIND
AND THERE ARE AREN’T MANY.
OKAY, SO NOW I WANT THE NEXT.
NOW, I HAVE TO ALSO--
THIS ONE ALSO DRIVES ME CRAZY.
UM, IF I LET THE MOVIE GO.
BUT, THE COOL THING HERE IS,
WITH THE CONFOCAL,
YOU CAN TAKE STACKS, RIGHT?
DIFFERENT LAYERS,
AND THEN YOU CAN PUT THEM
ON TOP OF ONE ANOTHER, RIGHT?
AND NOW YOU CAN ROTATE THEM
WITH STANDARD SOFTWARE, RIGHT?
AND SO, THIS IS 20 STACKS,
OKAY?
AND WHAT YOU CAN SEE-- OOPS.
AND-- IF I CAN DO THIS.
AND, WHAT YOU CAN SEE HERE--
STOP IT--
IS THAT YOU CAN ROTATE
WHEN THAT LOCATES
THE 20 STACKS EDGE ON.
YOU CAN ROTATE IT,
ROTATE IT, ROTATE IN,
THEN HERE--
OOPS DID I PASS IT?
YOU CAN GET A CUT
AT THE RIGHT ANGLE,
WHERE YOU SEE--
DO YOU SEE IT?
WHERE YOU SEE THE SQUARE LATTICE
COMING INTO FOCUS.
YOU HAVE TO CATCH IT
JUST RIGHT, OKAY?
AND THAT’S WHAT IS SHOWING
OVER HERE AND OVER THERE,
I GUESS, RIGHT?
AND THAT MEANS WHEN
YOU TAKE IT AND YOU ROTATE IT
TO THE RIGHT ANGLE,
AND THE ANGLE IS WELL DEFINED
FOR FC-FCC,
YOU SEE THIS FOURFOLD SYMMETRY,
WHICH YOU WOULD NEVER SEE
IN THE RANDOM PACKING--
IN THE RANDOM HEXAGONAL PACKING,
OR IN THE HCP.
SO, UM, LET’S SEE,
DID I WRITE THIS DOWN SOMEWHERE?
OH, I DID--
I FORGOT TO EMPHASIZE THAT.
IT TURNS OUT THAT-- WHAT--
HOW MUCH TIME DO I HAVE?
AM I RUNNING OUT?
>> IT’S LIKE FIVE MORE MINUTES.
>> OH, I’M SORRY.
DID I SPEND TOO MUCH--
>> [INDISTINCT]
I’D SAY LET PEOPLE LEAVE.
WE’LL KEEP RECORDING IT.
>> YEAH, OKAY, THAT’S FINE.
>> OKAY, SO I’LL SPEED UP.
ANYWAY, NOW THAT WE CAN SORT
OF-- NOW THAT--
THESE DAYS, COMPUTER SIMULATIONS
GOT RID OF THE GLASS,
WE LET THEM FIND THAT--
TRY AND FIND OUT
WHICH IS THE STABLE PHASE?
THE DENSITY OF HCP AND FCC
IS THE SAME,
BUT IT TURNS OUT,
FCC BEATS HCP BY TWO PARTS
IN A THOUSAND-- VERY, VERY
SMALL DIFFERENCE, OKAY?
NONETHELESS, OKAY?
WHAT YOU SEE IS THAT
THIS GUY, OKAY?
UM, IS SHOWING YOU THAT
YOU’VE GOT A HEXAGONAL PLANE.
YOU’VE GOT THE SQUARE PLANE
RIGHT HERE.
THAT’S LIKE LOOKING
AT THIS SURFACE
AND THIS SURFACE OF THE CRYSTAL,
AND SO, FCC CRYSTAL ACTUALLY
IS TRUE-- IS RIGHT,
AND, UM,
WE NOW CAN BELIEVE SIMULATIONS,
EVEN TO THAT ACCURACY.
THEY’VE-- FINALLY THE PICTURE
IS FINISHED AND DONE WITH.
FCC IS THE STABLE STRUCTURE
FOR HARD SPHERES--
TO THIS ANCIENT PROBLEM
OF HARD SPHERES.