Foldable substrates having a cavity filled with a polymer and methods of making

A method of making a foldable substrate comprising a substrate thickness a predetermined first transition region and a predetermined second transition region, the method comprising:

• ink-jet printing a plurality of shapes on a first major surface including a central portion of the foldable substrate, wherein the plurality of shapes are non-uniformly distributed over the first major surface in a predetermined pattern;
• etching the foldable substrate by contacting a central portion of the foldable substrate and the plurality of shapes with an etchant, the etching removes a portion of the foldable substrate to form a first central surface area recessed from the first major surface by a first distance and defining a first recess, the etching removes a portion of the foldable substrate to form a first transition surface area of the predetermined first transition region, and the etching removes a portion of the foldable substrate to form a third transition surface area of the predetermined second transition region;
• and
• disposing a first polymer-based portion in the first recess, a first polymer-based portion disposed in the first recess comprising a first contact surface facing the first central surface area and a second contact surface opposite the first contact surface, and an absolute value of a difference between a first refractive index of the foldable substrate and a second refractive index of the first polymer-based portion is about 0.1 or less,
• wherein the substrate thickness is in a range from about 80 micrometers to about 5 millimeters, the foldable substrate comprising a glass-based material or a ceramic-based material, and the foldable substrate comprises:
• a first portion comprising the substrate thickness between a first surface area of the first major surface and a second surface area of the second major surface:
• a second portion comprising the substrate thickness between a third surface area of the first major surface and a fourth surface area of the second major surface:
• the central portion comprising:
• a central thickness less than the substrate thickness and in a range from about 20 micrometers to about 200 micrometers defined between the first central surface area and a second central surface area opposite the first central surface area:
• the predetermined first transition region comprising the first transition surface area extending between the first surface area and the first central surface area with a first average angle relative to the first central surface area, and a thickness of the first transition region smoothly and monotonically decreases between the substrate thickness of the first portion and the central thickness of the central portion;
• and
• the predetermined second transition region comprising the third transition surface area extending between the third surface area and the first central surface area with a third average angle relative to the first central surface area, and a thickness of the second transition region smoothly and monotonically decreases between the substrate thickness of the second portion and the central thickness of the central portion,
• wherein a first polymer angle defined as an internal angle between the first major surface of the foldable substrate and the second contact surface of the polymer-based portion is in a range from about 178.3° to about 179.9°, and the first average angle is in a range from about 176.1° to about 179.9°.

A foldable apparatus comprising a foldable substrate, the foldable substrate comprising:

• a substrate thickness in a range from about 80 micrometers to about 5 millimeters defined between a first major surface and a second major surface opposite the first major surface, the foldable substrate comprising a glass-based material or a ceramic-based material;
• a first portion comprising the substrate thickness between a first surface area of the first major surface and a second surface area of the second major surface;
• a second portion comprising the substrate thickness between a third surface area of the first major surface and a fourth surface area of the second major surface;
• a central portion comprising:
• a central thickness less than the substrate thickness and in a range from about 20 micrometers to about 200 micrometers defined between a first central surface area and a second central surface area opposite the first central surface area;
• the first central surface area is recessed from the first major surface by a first distance and defining a first recess;
• a first transition region comprising a first transition surface area extending between the first surface area and the first central surface area with a first average angle relative to the first central surface area, and a thickness of the first transition region smoothly and monotonically decreases between the substrate thickness of the first portion and the central thickness of the central portion;
• and
• a second transition region comprising a third transition surface area extending between the third surface area and the first central surface area with a third average angle relative to the first central surface area, and a thickness of the second transition region smoothly and monotonically decreases between the substrate thickness of the second portion and the central thickness of the central portion,
• a first polymer-based portion disposed in the first recess comprising a first contact surface facing the first central surface area and a second contact surface opposite the first contact surface, and an absolute value of a difference between a first refractive index of the foldable substrate and a second refractive index of the first polymer-based portion is about 0.1 or less,
• wherein a first polymer angle defined as an internal angle between the first major surface of the foldable substrate and the second contact surface of the polymer-based portion is in a range from about 178.3° to about 179.9°, and the first average angle is in a range from about 176.1° to about 179.9°.